Mathematica Another bug? Weird integration results.

[Hepth]

I can't upload the notebook I guess, that would be a nice feature mods! (.nb extension)

But here is my code , there seems to be a problem with integrating separately and then combining.

$Assumptions = 0 < r < 1 && 0 < z < 1;
FUNCTION = Expand[-(Pi*(-1 + r)*(-12*z + r^2*z + r*(-12 + 11*z)))/(12*(r*(-1 + z) - z))];
temp1 = Table[Integrate[FUNCTION[[i]], z, Assumptions -> $Assumptions], {i, 1, Length[FUNCTION]}] // Total // Expand
temp2 = Integrate[FUNCTION, z, Assumptions -> $Assumptions] // Expand
temp1 /. {r -> 1/16., z -> 0.1}
temp2 /. {r -> 1/16., z -> 0.1}

So the problem is that if I choose each piece of the function, integrate them individually, its not the same result as if i do the whole integration.

This is on MM9 right now. Can anyone confirm this? My results are

0.297957 -0.620063 I
0.495329 -0.00321276 I

 

[Hepth]

Wow it really is just something with not fullsimplifying the function first :

FUNCTION = (-12*z + r^2*z + r*(-12 + 11*z))/(12*(r*(-1 + z) - z));
Integrate[   Simplify[FUNCTION,   0 < r < 1 && 0 < z < 1], z] /. {r -> 1/16, z -> 1/10} // N
Integrate[   FullSimplify[FUNCTION,   0 < r < 1 && 0 < z < 1], z] /. {r -> 1/16, z -> 1/10} // N

0.168179 -0.00109083 I

0.101165